One of the critical issues in healthcare management is the operating room (OR) scheduling problem. Solutions to this problem consider surgery durations and allocate elective surgeries to OR sessions in order to create surgical lists of high quality. Determining the quality of a surgical list is a key undertaking within OR scheduling and is the focus of this research. Currently, probability- and/or expectation-based measures of surgical lists are used instead of statistical distributions of surgery lists to measure quality. The use of multiple measures, e.g., a combination of expectation and probability to assess a surgical list, complicates OR scheduling, so we introduce a new single measure – the OR scheduling metric – for evaluating surgical lists before their realisations, i.e., for use within OR scheduling. We apply the OR scheduling metric to an actual elective dataset and use simulation to demonstrate its use, including customised scheduling rules. We recommend the adoption of a benchmarked OR scheduling metric by the elective surgical services in hospitals with expected practical benefits in the long run, i.e., simpler OR scheduling and more desirable room utilisation, to be similar to that observed in our simulations.

In this paper, we present a new model averaging technique that can be applied in medical research. The dataset is first partitioned by the values of its categorical explanatory variables. Then for each partition, a model average is determined by minimising some form of squared errors, which could be the leave-one-out cross-validation errors. From our asymptotic optimality study and the results of simulations, we demonstrate under several high-level assumptions and modelling conditions that this model averaging procedure may outperform jackknife model averaging, which is a well-established technique. We also present an example where a cross-validation procedure does not work (that is, a zero-valued cross-validation error is obtained) when determining the weights for model averaging.

We present an elective surgery redesign project involving several New Zealand hospitals that is primarily data-driven. One of the project objectives is to improve the predictions of surgery durations. We address this task by considering two approaches: (a) linear regression modelling, and (b) improvement of the data quality. For (a) we evaluate the accuracy of predictions using two performance measures. These predictions are compared to the surgeons' estimates that may subsequently be adjusted. We demonstrate using the historical surgical lists that the estimates from our prediction techniques improve the scheduling of elective surgeries by minimising the occurrences of list under- and over-runs. For (b), we discuss how the surgical data motivates a review of the surgery procedure classification which takes into account the design of the electronic booking form. The proposed hierarchical classification streamlines the specification of surgery types and therefore retains the potential for improved predictions.

The power domination problem aims to and the minimum number of phase measurement units (PMUs) required in order to observe the entire electric power system. Zhao and Kang [6] remarked that there is no known nonplanar graph of diameter two with a power domination number that is arbitrarily large. In this note, we show that the power domination number of such graphs can be arbitrarily large.

The degree of accuracy in surgery duration estimation directly impacts on the quality of planned surgical lists. Model selection for the prediction of surgery duration requires technical expertise and significant time and effort. The result is often a collection of viable models, the performance of which varies across different strata of the surgical population. This paper proposes a prediction framework to be used after a comprehensive model selection process has been completed for surgery duration prediction. The framework produces a partition of the surgical cases and a “hybrid model” that allocates different predictors from the collection of viable models to different parts of the surgical population. The intention is a flexible prediction process that can reassign models and adapt as surgical processes change. The framework is tested via a simulation study, and its utility is demonstrated by predicting surgery durations for Ear, Nose and Throat surgeries in a New Zealand hospital. The results indicate that the hybrid model is effective, performing better than standard model selection in two of the three simulation studies, and marginally worse when the selected model was the true underlying process.

We implement jackknife model averaging (JMA) and a new prediction technique—hybrid-boost model averaging (HbMA)—to a surgical dataset that includes categorical explanatory variables. The model requirements for HbMA are different to that for JMA. HbMA generally does not require decent models to be included in the model average. However, the utility of HbMA is limited by the possibility of multiple solutions for the HbMA weights. Both model averaging approaches are comparable under the appropriate conditions. Among all the model averages considered, the best jackknife model average gives slightly better predictions of the surgery durations than the best hybrid-boost model average when evaluated on our surgical dataset. Finally, we discuss several methods that may further improve the performance of HbMA.

We review recent results on the power domination problem of graph products and establish improved results for some families of graph products, namely, , , Pn ⊠ Pm, Pn ⊠ Cm and Cn ⊠ Cm. We also characterize graphs G and H for which the power domination number of the Cartesian product of G and H, which is denoted as , is 1.

The surgical department is a critical unit that oversees multiple surgical-based clinical pathways and works with various other units in a hospital. This department faces numerous challenges relating to variability in demand and management of resources. The aim of this article is to review the application of validated simulation models on hospital-wide surgical services. Each of these models is broadly classified by (i) simulation method and (ii) level of detail given to the management of “patient pathways” and “staff workflows”. We remark that very few studies have given attention to the management of staff workflows in their validated simulation models.

In this paper, we first give a brief survey on the power domination of the Cartesian product of graphs. Then we conjecture a Vizing-like inequality for the power domination problem, and prove that the inequality holds when at least one of the two graphs is a tree.

In this paper, we present some new families of graceful join of graphs and propose a few unsolved problems in this area.

Let γb(G1□G2) denote the broadcast domination number for the Cartesian product of two graphs G1 and G2. In this paper, we evaluate the value of γb(G1□G2), where Gi is either a path, cycle, star, or complete graph.

A broadcast on a graph G is a function f : V (G) ! f0;1;:::;diam(G)g such that for every vertex v 2 V (G), f(v) e(v), where diam(G) is the diameter of G, and e(v) is the eccentricity of v. In addition, if every vertex hears the broadcast, then the broadcast is a dominating broadcast. The cost of a broadcast f is the value (f) = ∑ v2V (G) f(v). In this paper we determine the minimum cost of a dominating broadcast (also known as the broadcast domination number) for a torus Cm □ Cn.

Let γb(G) denote the broadcast domination number for a graph G .I n [Discrete Applied Math. 154 (2006), 59–75], Dunbar et al. determined the value of γb(G), where G is the Cartesian product of two paths. In this paper, we evaluate the value of γb(G), whenever G is the strong product, the direct product and the lexicographic product of two paths.